Abstract
We consider two generalizations of the
= 6 superconformal Chern-Simons-matter theories with gauge
group U(N) × U(N). The first generalization is
to = 6 superconformal U(M) × U(N) theories,
and the second to = 5 superconformal
O(2M) × USp(2N) and O(2M+1) × USp(2N) theories.
These theories are conjectured to describe
M2-branes probing C4/Zk in the unitary case,
and C4/
k in the orthogonal/symplectic case,
together with a discrete flux, which can be interpreted as
|M−N| fractional M2-branes localized at the orbifold singularity.
The classical theories with these gauge groups have been
constructed before; in this paper we focus on some quantum
aspects of these theories, and on a detailed description of their
M theory and type IIA string theory duals.
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